Chronological overview

I. Estimation

• Get data.
• Estimate parameters of stock prices; (52) and (53).
• Estimate parameters of interest rate dynamics (cf. Subsection 4.1).
• Compute the historical time series $x_{i,m}$ ($m \leq 0$) by (57).
• Solve equations (50) and (49) for the historical $N_{j,m}$ ($m \leq 0$).
• Compute the covariance matrix $\widehat{\Sigma}$; (54).
• Compute the Cholesky decomposition of $\widehat{\Sigma}$; (47).

II. Simulation

• Simulate future i.i.d. normal random variables and plug them into (48) to get the simulated $N_{i,m}$ ($m > 0$).
• Plug the $N_{i,m}$ into (50) and (49) to get the simulated scenario of stock prices and interest rate model factors $x_{i,m}$ ($m > 0$).
• Plug the factors $x_{i,m}$ into (38) or (39) to get spot rates or bond prices.
• Reiterate the above three steps to get a large set of market scenarios.

III. Evaluation

• Choose (or assume to be given) a certain portfolio.
• Compute portfolio values (e.g. by (1)) using the scenarios generated in step II.
• Compute the risk and performance measures (10), (12) and (15) by the empirical portfolio distributions obtained; cf. (31) to (33).
• If necessary, compute the partial derivatives (23), (24) and (25).

IV. Optimization

• Use a GS or SI method repeating step III for each new portfolio.

Note that the simulation procedure (=scenario generation; step II) must only be done once. The optimization loops use the same set of scenarios for alternating portfolios.